A most common use case for javascript buttons is a simple field update, onclick of the button a field/fields are updated and the page is refreshed.

With the onset of Lightning javascript buttons are no longer supported and hence have to be replaced. A simple solution would be to use Visualforce which works both in the Lightning UI and classic. However, there is a known issue where the page does not reload/get the updated information when you a do a page redirect using PageReference in Visualforce.

While the workaround mentioned does address the issue, it should be noted that any email templates associated should be taken care. Make sure you check these areas and move all associated email templates into a public folder.